InferenceEvolve: Towards Automated Causal Effect Estimators through Self-Evolving AI

Can Wang; Hongyu Zhao; Yiqun Chen

cs.AIApr 5, 2026

InferenceEvolve: Towards Automated Causal Effect Estimators through Self-Evolving AI

Authors: Can Wang, Hongyu Zhao, Yiqun Chen

Organizations: Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA · Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218, USA

Abstract

Causal inference is central to scientific discovery, yet choosing appropriate methods remains challenging because of the complexity of both statistical methodology and real-world data. Inspired by the success of artificial intelligence in accelerating scientific discovery, we introduce InferenceEvolve, an evolutionary framework that uses large language models to discover and iteratively refine causal methods. Across widely used benchmarks, InferenceEvolve yields estimators that consistently outperform established baselines: against 58 human submissions in a recent community competition, our best evolved estimator lay on the Pareto frontier across two evaluation metrics. We also developed robust proxy objectives for settings without semi-synthetic outcomes, with competitive results. Analysis of the evolutionary trajectories shows that agents progressively discover sophisticated strategies tailored to unrevealed data-generating mechanisms. These findings suggest that language-model-guided evolution can optimize structured scientific programs such as causal inference, even when outcomes are only partially observed.

Figures & tables

Dataset	Baseline	Mode	Best	Mean $\pm$ SE	% beat	Best $\Delta$ (%)
IHDP $\sqrt{\mathrm{PEHE}}$	2.411 (BART)	True	1.222	$1.392\pm 0.021$	100%	49.3%
		Proxy	1.034	$1.632\pm 0.311$	83%	57.1%
ATE error	0.110 (BART)	True	0.063	$0.081\pm 0.005$	100%	42.9%
		Proxy	0.074	$0.084\pm 0.003$	100%	33.0%
ACIC 2016 $\sqrt{\mathrm{PEHE}}$	1.283 (Causal forest)	True	0.858	$1.011\pm 0.042$	100%	33.1%
		Proxy	1.504	$2.037\pm 0.196$	0%	$-$ 17.2%

Table 1: Best evolved estimators versus baseline methods. The baseline column gives the candidate used for each row: the strongest package baseline in Fig. 2 . Best evolved and best

\Delta

(%) refer to the single best final program under each guidance mode, where positive best

\Delta

indicates percent error reduction relative to the row-specific baseline comparator. Mean

\pm

SE and % beat summarize the performance across all parameter settings for InferenceEvolve .

Dataset	Dominant family	Typical refinements during evolution	Within-dataset TF-IDF	Closest official reference	Median closest-ref. emb. cosine
ACIC 2022	TWFE / DiD / panel fixed-effects estimators	Pre-period anchoring, detrending, patient weighting, clustered or small-sample inference, and coverage-oriented calibration	$0.336\pm 0.110$	IPW	0.585
ACIC 2016	Meta-learners with boosting and DR correction	Cross-fitting, propensity clipping, one-hot encoding of mixed covariates, X-learner or DR-learner structures, and AIPW-style aggregation	$0.353\pm 0.173$	DR-learner	0.678
IHDP	T-/X-learners with boosted or forest nuisance models	Outcome-model tuning, DR pseudo-outcome refinement, ATE calibration, and more stable nuisance estimation	$0.415\pm 0.244$	Causal forest	0.691
LaLonde	Weighting and DR hybrids for observational bias correction	Propensity weighting, AIPW/DR correction, adaptive regularization, and ensemble smoothing under small-sample instability	$0.331\pm 0.116$	DR-learner	0.707

Table 2: Representative solution families discovered by evolution. Final programs cluster into dataset-specific estimator families with recognizable refinement patterns. Similarity values report mean within-dataset TF-IDF cosine similarity among final programs (

\pm

s.d.) and the median closest official-reference embedding cosine. The “closest official reference” column should be interpreted as the nearest single wrapper in embedding space rather than as a second family label: for example, ACIC 2022’s weighting-heavy panel estimators sit nearest the IPW wrapper, whereas IHDP’s tree- and forest-based nuisance structure pulls that benchmark closest to the causal-forest wrapper.

Parameter	Value
Evolutionary search
Maximum iterations	100
Population size (MAP-Elites)	60
Number of islands	4
Archive size per island	25
Elite selection ratio	0.3

Supplementary Table 1: Complete hyperparameter configuration. Parameters held constant across the 96-run factorial experiment unless noted. Factorial factors indicated with

\dagger

Model	Attempts	RMSE	Coverage	Method
Claude Sonnet 4	2	89.24	0.12	Weighted AIPW w/ RF
GPT-5	1	33.05	0.40	Patient-weighted TWFE DiD
GPT-4o	1	39.21	0.36	DiD + regression adjustment
Grok 4 Fast	3	89.24	0.22	Diff-in-means w/ bootstrap
Qwen3-Coder	1	68.93	0.30	Weighted TWFE (clustered)
DeepSeek v3.1	2	19.44	0.02	Weighted FE w/ clustered SEs

Supplementary Table 2: Full zero-shot results on ACIC 2022 (50 replicates). Seven LLMs evaluated under identical conditions. Each model was given the same structured prompt containing the data schema, causal assumptions, evaluation criteria, and a six-row data preview. Models were allowed up to five attempts to produce a valid program passing a 180 s warm-up test on a single replicate.

Model	Attempts	$\sqrt{\text{PEHE}}$	$\|\text{ATE error}\|$
Claude Sonnet 4	1	$2.40\pm 0.55$	$0.103\pm 0.013$
GPT-5	1	$5.68\pm 0.73$	$0.292\pm 0.030$
GPT-4o	1	$1.86\pm 0.38$	$0.104\pm 0.014$
Grok 4 Fast	1	$1.86\pm 0.38$	$0.106\pm 0.014$
Qwen3-Coder	2	$3.11\pm 0.73$	$0.489\pm 0.141$
DeepSeek v3.1	2	$2.02\pm 0.34$	$0.103\pm 0.018$

Supplementary Table 3: Full zero-shot results on IHDP (50 replicates). Seven LLMs evaluated under identical conditions. Method sketches are determined by inspecting the generated code. Means

\pm

SE are computed across 50 replicates with ground-truth potential outcomes.

Component	Models / inputs	Retrieval rule or shared prompt
Program pool	28 baselines, 96 true-evolved finals, 48 proxy-evolved finals	One final snippet per run from the zero-shot baseline pool, the true-score final-program pool, and the proxy-score final-program pool. The exact 172-program manifest is archived alongside the analysis outputs.
Translation	GPT-5, Gemini 2.5 Pro, Claude Sonnet 4.5	Shared system and user template shown below; each prompt supplied the dataset name, source label, and full program text, and asked for a single manuscript-style methods paragraph.
Judge panel	GPT-5, Gemini 2.5 Pro, Claude Sonnet 4.5	Shared JSON-returning review template shown below; each prompt asked for family assignment, nearest known method, complexity, pipeline steps, and novel components before cross-model aggregation.
Embedding sensitivity	OpenAI main; Qwen sensitivity	All manuscript figures and tables use text-embedding-3-large . The same nearest-reference and within/between-program summaries were rerun with Qwen3-Embedding-0.6B only as a sensitivity analysis.

Supplementary Table 4: Program-analysis inputs and prompt summaries. Exact code sources and shared prompt templates for the program-analysis pipeline.

Family	Wrapper	Package	Commit-pinned upstream example	Commit
T-learner	T-Learner (EconML TLearner)	EconML	https://github.com/py-why/EconML/blob/b0404c02be5af1f9a2cbc2bd66d9b47e38c6ebb4/econml/metalearners/_metalearners.py#L54-L62	b0404c0
X-learner	X-Learner (EconML XLearner)	EconML	https://github.com/py-why/EconML/blob/b0404c02be5af1f9a2cbc2bd66d9b47e38c6ebb4/econml/metalearners/_metalearners.py#L328-L336	b0404c0
DR-learner	DR-Learner (EconML DRLearner)	EconML	https://github.com/py-why/EconML/blob/b0404c02be5af1f9a2cbc2bd66d9b47e38c6ebb4/econml/dr/_drlearner.py#L542-L555	b0404c0
IPW	IPW (zEpid IPTW)	zEpid	https://github.com/pzivich/zEpid/blob/16a0f96f8b2c65df8715085801f21757d1478e1e/zepid/causal/ipw/IPTW.py#L85-L88	16a0f96
OLS	OLS (statsmodels OLS)	statsmodels	https://github.com/statsmodels/statsmodels/blob/184e7f8e5725613ba64cbabc9bf0a33354e1d95e/examples/python/ols.py#L31-L37	184e7f8
AIPW	AIPW (zEpid AIPTW)	zEpid	https://github.com/pzivich/zEpid/blob/16a0f96f8b2c65df8715085801f21757d1478e1e/zepid/causal/doublyrobust/AIPW.py#L74-L77	16a0f96

Supplementary Table 5: Commit-pinned upstream sources for the official reference library. Each normalized estimate(df) wrapper used in the reference-matching analysis was adapted from the corresponding maintainer example at the listed commit-pinned URL.

Comparison	Mean $\pm$ SD	$n$ pairs
Within ACIC 2022	$0.336\pm 0.110$	276
Within ACIC 2016	$0.353\pm 0.173$	276
Within IHDP	$0.415\pm 0.244$	276
Within LaLonde	$0.331\pm 0.116$	276
ACIC 2022 vs. IHDP	$0.140\pm 0.053$	576
ACIC 2016 vs. IHDP	$0.352\pm 0.186$	576

Supplementary Table 6: Code similarity among final programs. TF-IDF cosine similarity between pairs of final evolved programs. Within-dataset similarity is consistently higher than between-dataset similarity, confirming genuine dataset-specific adaptation.

Dataset	Correlation	$n$	$p$ -value
IHDP	0.97	4	0.03
LaLonde-Norm	0.77	4	0.23
ACIC 2016 ∗	0.50	3	0.67
ACIC 2022 (DR-DID hit-rate vs. true coverage)	0.99	76	$1.3\times 10^{-67}$

Supplementary Table 7: Proxy metric validation. For IHDP, LaLonde-Norm, and ACIC 2016, values report Pearson correlation between matched final-run proxy combined scores and true combined scores. For ACIC 2022, values report Spearman correlation between the DR-DID hit-rate component and true coverage across checkpoint reevaluations.

Iter.	RMSE	Cov.	Ridge	Cov. enc.	Pre-mean	Trend	Post-only	CI adj.
0 (init)	33.1	0.40	—	—	—	—	—	—
2	31.7	0.55	✓	✓	—	—	—	—
14	28.7	0.55	—	✓	✓	—	—	—
16	27.1	0.75	—	✓	✓	—	—	✓
22	18.5	0.95	—	✓	✓	—	✓	✓
52	15.3	0.90	—	✓	✓	✓	✓	✓

Supplementary Table 8: ACIC 2022 feature progression. Each row is a new-best checkpoint. The agent progressively discovers DiD logic, pre-mean adjustment, and trend correction.

Iter.	Method	$\sqrt{\text{PEHE}}$	$\|\text{ATE error}\|$	Combined
Init	X-Learner (GBM, cross-fitted)	1.225	—	baseline
Early	X-Learner + RF propensity (local weighting)	1.028	0.105	0.579
Final	X-Learner (GBM + RF PS)	1.028	0.105	0.579

Supplementary Table 9: ACIC 2016 evolution checkpoints. Best-run trajectory (Gemini,

\lambda=0.2

, split 20:80). The agent refines a simple X-learner into a random-forest propensity-weighted X-learner with local blending.

Iter.	Method	$\sqrt{\text{PEHE}}$	$\|\text{ATE error}\|$
Init	X-Learner (GBM, cross-fitted, constant $g$ )	1.613	0.116
Early	GBM+Ridge ensemble ( $0.7/0.3$ ) + polynomial features	$\approx$ 1.4	$\approx$ 0.10
Mid	+ MLP treatment effect models (TARNet-style)	$\approx$ 1.3	$\approx$ 0.10
Final	TARNet-style X-learner + ensemble + adaptive- $g$	1.253	0.115

Supplementary Table 10: IHDP evolution checkpoints. Best-run trajectory (GPT-5,

\lambda=0.2

, split 20:80). The agent augments the X-learner with an ensemble backbone, neural network treatment effect models, and adaptive propensity weighting.

Iter.	Method	$\sqrt{\text{PEHE}}$	$\|\text{ATE error}\|$
Init	X-Learner (GBM, cross-fitted, constant $g$ )	—	—
Early	+ Cross-fitted propensity model + DR pseudo-outcomes	$\approx$ 1.5	$\approx$ 0.20
Mid	X-learner + R-learner blend with AIPW	$\approx$ 1.4	$\approx$ 0.17
Final	CF X+R blend, AIPW-calib (GBR+Ridge)	1.359	0.161

Supplementary Table 11: LaLonde evolution checkpoints. Best-run trajectory (GPT-5,

\lambda=0.2

, split 20:80). The agent blends X-learner and R-learner components with AIPW calibration.

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Causal effect estimation measures how outcomes would change under interventions, using experiments or observational data and explicit assumptions.

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CausalEvolve: Towards Open-Ended Discovery with Causal Scratchpad

Yongqiang Chen, Chenxi Liu, Zhenhao Chen, Tongliang Liu+2

MBZUAI · Carnegie Mellon University · TMLR Group, Hong Kong Baptist University+1

AI Agents for Scientific Discovery Large Language Model-Guided Scientific Discovery Open-Ended Evolution Large Language Model-Guided Optimization

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Evolve-based agent such as AlphaEvolve is one of the notable successes in using Large Language Models (LLMs) to build AI Scientists. These agents tackle open-ended scientific problems by iteratively improving and evolving programs, leveraging the prior knowledge and reasoning capabilities of LLMs. Despite the success, existing evolve-based agents lack targeted guidance for evolution and effective mechanisms for organizing and utilizing knowledge acquired from past evolutionary experience. Consequently, they suffer from decreasing evolution efficiency and exhibit oscillatory behavior when approaching known performance boundaries. To mitigate the gap, we develop CausalEvolve, equipped with a causal scratchpad that leverages LLMs to identify and reason about guiding factors for evolution. At the beginning, CausalEvolve first identifies outcome-level factors that offer complementary inspirations in improving the target objective. During the evolution, CausalEvolve also inspects surprise patterns during the evolution and abductive reasoning to hypothesize new factors, which in turn offer novel directions. Through comprehensive experiments, we show that CausalEvolve effectively improves the evolutionary efficiency and discovers better solutions in 4 challenging open-ended scientific tasks.

Abstract

Causal Effect Estimation

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